Had Lampard led Chelsea to the Champions League final, the Englishman would have been in contention to remain at Stamford Bridge in the long term, but the 4-0 aggregate defeat to Real Madrid in the quarter-finals meant that any possibility of a permanent second stint was ruled out.
At the same time, Pochettino became the clear favourite to return to the Premier League having previously managed fellow London club Tottenham Hotspur.
According to The Guardian, there is now every expectation that the Argentine will be soon be confirmed as the new head coach.
While it is stated that discussions and negotiations are far from complete, it is suggested that an unforeseen change of heart from either party would prevent a deal from being finalised.
With Chelsea having just seven Premier League fixtures left and with little but Europa Conference League qualification to play for, an announcement may be made before the end of the season.
Pochettino has spent this season out of work having been relieved of his duties at Paris Saint-Germain last year, a consequence of their last-16 exit from the Champions League.
Nevertheless, the 51-year-old remains highly regarded in Europe, helped by his stint at Spurs where the club became Premier League title challengers and reached a Champions League final.
In recent days, it has also been claimed that a number of Chelsea players would support the appointment, arguably a key factor when it comes to Boehly and co making their final choice.
Should Pochettino arrive in West London, he will be tasked with overseeing a much-changed squad, a result of Chelsea needing to facilitate a wide array of sales to comply with FFP.